Here is a link to the article in which Leon Foucault first
described his original method of making silvered, parabolized,
telescopic mirrors on polished glass. I translated the
article into English. As far as I know, mine is the only such translation.
If you read the article, you will notice that Foucault's methods
are not exactly the same as what modern-day optical workers know
as the Foucault test. They also involve testing at the two foci of
an ellipse, and also foreshadow what we call the Ronchi test. Leon Foucault
- original knife-edge article, in English

I run a weekly workshop under
the auspices of the National Capital Astronomers (NCA) for making
astronomical telescopes at the Chevy Chase Community Center
(CCCC) in Washington, DC. It's every Friday evening from 6:30 to 9:30.
attendance is free, and you only pay for materials. Follow this link
for more details on this workshop:. NCA/CCCC
Mirror Making Workshop informationWhy make your own telescope, when you can purchase
one?Because you can make a BETTER one, for less money,
too!Why be
an amateur telescope maker (an ATM)

Here is a link to a field trip
that I put together for my students at Alice Deal Junior High
School in Washington, DC, called "Math On the Mall - And Beyond."
I was fortunate to have had the enthusiastic cooperation of nearly
20 chaperones for over 100 students. I got the idea for my trip
from the field trip for math teachers that Drs. Florence Fasanelli and Fred
Rickey (and others) assembled over many
years. On our trip, students and parents looked at a large number of
things of mathematical and historical interest, even while walking
to and from the subway. We also saw special exhibitions of original
prints and drawings by M.C. Escher and rare old books and notebooks
by Newton, Euler, Euclid, Banneker, and others, courtesty of the staff
of the special collections libraries at the National Gallery of Art and
the Museum of American History We also saw many other things in and around
the buildings on the National Mall and the Smithsonian Institution and
National Gallery of Art. This is a large PDF file, 31 pages, 340 kB.
With
this link, look near the bottom of the pageThis
is the PDF file itself.

Here is a link to a somewhat-annotated
list of books on math and/or science. Look at this bibliography
if you are a teacher or a student looking for something interesting
to read in either field. It is broken down by subject area. In
my 8th/9th grade algebra and geometry classes I have asked students
to read two of these books each year, and to write reports
on them. Many of the results have been very good. Brandenburg's
list of Math, Science Books

I have
been involved in a trans-atlantic geometry project
known as Geometrix. This is a piece of software
that does just about everything that other dynamic geometry
programs do, but it has two very important features that the other
programs do not have:

First, in construction mode,
it allows the teacher to pose a particular
construction task for the student, and to give
students feedback in real time (hints, suggestions, kudos)
as they progress towards completing the construction The teacher
can also specify what tools will be available for the construction. Thus,
you can make it just like a 'compass and straightedge' construction,
or you can allow the student to be able to make parallel lines, angle
bisectors, or even centroids, simply by clicking on the appropriate
button. The constructions can be either simple or tricky, depending.

Secondly, in proof mode,
it allows the student to work his or her way through a proof.
The program checks all the steps of a proof as the student
performs them and gives immediate feedback as to whether the
step is justifiable or not. (The entire concept of proof is probably
the hardest one for most students!) Proof exercises specify which theorems,
postulates, properties, and definitions are available for use by the
student, but the student can work through the proof in any one of a
very large number of different possible logical paths.

The program was written by
Jacques Gressier of the Academy of Lille, and the
original exercises were written in French (and designed for the
French national curriculum) by Bernard Montuelle and
Danièle Fosseux. (All 3 live and work in northern France, in the region near
Boulogne-sur-Mer, a bit south of Calais). I (Guy Brandenburg)
heard about the program via one of the math-teacher list-serves
on the Math Forum, and was intrigued. I eventually translated the program's
interface into American English, adapted or wrote from scratch 200
construction and proof exercies, and wrote the 80-plus-page manual.
It helped a lot when I went to France and met with the original authors
(and enjoyed the wonderful French hospitality of the lovely Montuelle
family!) to learn more about how it works - some things are much harder
to communicate by e-mail than in person. (My French is not too bad - I went
to school for two widely separated years as a youngster and earned a Baccalauréat
in Mathématiques Elémentaires in 1967.) The American version of the program is published by Sunburst.
The French version is published by CDE4. Here are links to Geometrix.
Jacques
Gressier's Web Pages on Geometrix (in French and English)
and Sunburst
catalog page on Geometrix and CDE4 website (in French)

The following diagram is a classic
of chaos theory. It shows what happens (after about 100 iterations)
when the output from the function a=k*b*(1-b)gets fed into itself, as k varies. As k gets larger, you start to get two different levels of output, then four different levels, then 8,
then you get extremely strange,
chaotic behavior. Writing the code to implement this chaotic diagram is actually very easy
(you can do it on a graphing calculator), but I used Fractint to
create this.

click on the thumbnail sketch above
to see a full-sized diagram with more detail.